1. Field of the Invention
This invention relates generally to the field of geophysical prospecting. More particularly, the invention relates to the field of seismic data acquisition. Specifically, the invention is a method of seismic source monitoring using modeled source signatures with calibration functions.
2. Description of the Related Art
Marine seismic exploration typically employs a submerged seismic source towed by a ship and periodically activated to generate an acoustic wavefield (a “shot”). The wavefield may be generated by a small explosive charge, an electric spark or arc, a vibrator, or, typically, a gun. The gun may be a water gun, vapor gun, or, most typically, an airgun. Each airgun contains a volume of air typically compressed to about 2000 psi (pounds per square inch) or more. An airgun abruptly releases its compressed air to create an air bubble, leading to an expanding sound wave in the water. The resulting wave front propagates downwardly into the earth beneath the water, reflects from subterranean earth layers, and returns upwardly toward the water surface. Seismic receivers, which are typically streamers of hydrophones that are also submerged and towed by the same or another ship, detect the reflected wave fronts, convert the detected wave fronts to electrical signals, and transmit those signals to a ship for storage and processing.
When a seismic source is triggered, it produces a complex output pressure pulse in the water. In an idealized situation in which the seismic source is a point source, such as a single airgun, and there is no sea surface, the emitted wave front is independent of direction and distance, except for spherical spreading. Converted to an electrical signal, the output pulse of an airgun would consist of a short wave train whose envelope displays an initial short, fast, positive rise in amplitude followed by several rapidly-decaying oscillations. The recorded wave train is called the signature of the seismic source.
In practice, a sea surface exists and is typically only meters away from the seismic source. The acoustic wave generated by the seismic source radiates by spherical spreading in all directions such that there is a downwardly traveling component as well as an upwardly traveling component. The water-air interface at the sea surface has a reflection coefficient typically close to a value of −1. The upwardly traveling component of the acoustic wave is reflected by the water surface and is reversed in polarity to become another downgoing component. This additional downgoing component is generally referred to as a “ghost”. The ghost interferes with the direct wave to complicate the source signature.
Typically, a seismic source consists not of a single element, but of a spatially-distributed array of elements that generate direct arrivals plus the ghost components. This is particularly true of airguns, currently the most common form of marine seismic source. The spatial dimensions of an array of source elements may be comparable to the wavelengths of the acoustic waves themselves within the useful seismic frequency passband. Thus, there is no single source signature for an array. Rather, the source signature of an array in the near-field becomes a continuous function of both direction and distance. At distances large compared with the array dimensions, the dependence on distance in any particular direction becomes negligible. This region is called the far-field. It is the far-field signature that is useful for seismic data processing. For arrays of airguns, which typically extend over spatial dimensions of about 20 meters by 20 meters, the distance to the far-field is on the order of 250 meters.
Although modem airguns produce stable wavefields in a laboratory situation, the wavefields produced by arrays of airguns deployed at sea are not so stable. In a marine environment, the wavefields of airgun arrays vary from shot to shot because of physical factors such as airgun drop-outs; sea surface conditions affecting the ghost; and variations in the array geometry, airgun depth, pressure, airgun timing, water velocity, or sea temperature. If these source variations could be monitored accurately, the source variation data could be used to significantly enhance the quality of the resultant seismic data. Correcting for source variations may be particularly important in situations such as four-dimensional or time lapse seismic, such as reservoir monitoring. In these situations, very small differences in seismic data sets may otherwise be swamped by the source variations.
Shot to shot variations in marine seismic sources are not often monitored, primarily because it is difficult to do. However, methods of seismic source monitoring are currently in use. A first method, the far-field method, typically employs measurement of the vertically traveling signature with a far-field hydrophone. The far-field method, however, is unreliable because the position of the sensor drifts, only a single point in the wavefield is measured, and it is difficult to position the sensor (hydrophone) the required distance from the source. The far-field method often requires moving the seismic survey vessels and equipment to deeper waters to make the far-field measurements. Thus, the far-field method is difficult and expensive to do.
A second method of seismic source monitoring, the near-field method, employs measurement of near-field signatures, which can be analyzed to calculate the whole wavefield of the array. A primary example of this second method is known to those of ordinary skill in the art as the notional source method. A notional source signature is a normalized, idealized source signature that would be measured by a hydrophone at one meter distance from an airgun, if there were no surface reflection and no relative motion between the airgun bubble and the hydrophone. See, for example, the following two publications. The first publication is Ziolkowski, A., Parkes, G., Hatton, L., and Haugland, T., “The signature of an airgun array: Computation from near-field measurements including interactions”, Geophysics, Vol. 47, No. 10 (Oct. 1982), pp. 1413–1421. The second publication is Parkes, G., Ziolkowski, A., Hatton, L., and Haugland, T., “The signature of an airgun array: Computation from near-field measurements including interactions—Practical considerations”, Geophysics, Vol. 48, No. 2 (Feb. 1984), pp. 105–111.
The first publication, Ziolkowski et al. (1982), describes a theory of the interactions between bubbles produced by airguns in an array. Assuming that the bubbles are small compared with the wavelengths of seismic interest, the array of interacting oscillating bubbles is equivalent to a “notional” array of non-interacting oscillating bubbles. If there are n airguns in the array, then n independent measurements of the near-field pressure field of the full array may be used to determine the n notional source signatures. The signature of the array at any point in the water may then be calculated by linear superposition of these n notional source signatures. A spherical correction is also applied, in which the notional source signatures are scaled and time delayed relative to each other according to distance and direction. However, the number of near-field measurements must not be less than the number n of airguns in the array.
The second publication, Parkes et al. (1984), refines the solution of Ziolkowski et al. (1982) for the signature of an interacting array of airguns. An iterative technique is applied to calculate notional source signatures from the near-field measurements using hydrophones placed close (one meter) to each airgun. The amplitude variation effects of the forward motion of the hydrophones and the upward motion of the airgun bubbles with respect to each other are handled in a linear velocity model. However, continuous recording of the near-field signatures is required to recompute the wavefield if the radiation of the airgun array changes or becomes unstable.
The notional source method is further discussed in U.S. Pat. Nos. 4,476,550; 4,476,553 and 4,868,794. The first of these patents is U.S. Pat. No. 4,476,550, “Determination of far field signatures, for instance of seismic sources”, filed Aug. 25, 1981 and issued Oct. 9, 1984 to Ziolkowski, A. M. and Stoffa, P. L. The second patent, also issued on Oct. 9, 1984, is U.S. Pat. No. 4,476,553, “Method of determining the signatures of arrays of marine seismic sources”, issued to Ziolkowski, A., Hatton, L., Parkes, G., and Haugland, T. The third patent, issued to the same inventors as the '553 patent, is U.S. Pat. No. 4,868,794, “Method of accumulation data for use in determining the signatures of arrays of marine seismic sources”, issued Sep. 19, 1989.
The first patent, the Ziolkowski et al. '550 patent, discloses a method used with towed marine seismic streamers for ascertaining the far-field signature of an array of airguns, each of which is small compared with the wavelength of the highest frequency of interest. The airguns are fired so that interactions between the airguns are kept negligible, by either separation in time or separation in space. For separation in time, the airguns are fired sequentially so that each airgun generates all its significant radiation before the next airgun is fired. For separation in space, the airguns are fired more than one at a time, but are separated by a distance of at least one wavelength of the lowest frequency of interest. The far-field signature of each unit is measured by a pressure-sensitive detector close to the airgun but in a region where the phase spectrum of the pressure field is independent of azimuth and range. The far-field signature of the array is derived from the measured signatures by summation.
The second and third patents, the Ziolkowski et al. '553 and '794 patents, disclose a method for determining the far-field signature of an array of n airguns. The array is actuated and the emitted pressure wave is measured by n hydrophones at n independent points whose positions with respect to the array are known. The n measurements are processed to form n simultaneous equations, which are then solved to produce n notional signatures of the n sources. Solving the simultaneous equations takes into account the interactions between the airguns. The signature of the entire array is then determined by superposing the n notional signatures.
The notional source method, however, has some intrinsic practical difficulties. As described in the Ziolkowski et al. (1982) publication, the number of seismic sources (airguns) must equal the number of independent measurements (hydrophones), to provide n well- determined simultaneous equations to solve. Thus, all n airguns and all n hydrophones must function at all times. In addition, the notional source method assumes that the water-air interface at the sea surface is a good planar reflector with a reflection coefficient close to −1. Otherwise, as described in the Ziolkowski et al. '553 and '794 patents, the number of unknown variables doubles to 2n, which means that the number of hydrophones must double to 2n.
Furthermore, the notional source method typically uses hydrophones approximately one meter from each airgun, as described in the Parkes et al. (1984) publication. A hydrophone placed near the airgun array records the primary source signature from the airgun plus a much smaller ghost reflection from the sea surface. Additionally, each hydrophone records contributions from all the surrounding airguns. Both the ghost reflections and the relative motion between the hydrophones and the bubbles created by the hydrophones must be accounted for in the notional source method. Thus, the notional source method requires precise measurements of the separation between airguns and hydrophones as well as precise measurements of the spacing between airguns in the array.
Thus, a need exists for a method for determining an accurate far-field seismic source signature for an array of seismic sources.